Strong consistency of multivariate spectral variance estimators in Markov chain Monte Carlo

Dootika Vats, James M. Flegal, Galin L. Jones

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate nature has so far been ignored in the MCMC community. We present a class of multivariate spectral variance estimators for the asymptotic covariance matrix in the Markov chain central limit theorem and provide conditions for strong consistency. We examine the finite sample properties of the multivariate spectral variance estimators and its eigenvalues in the context of a vector autoregressive process of order 1.

Original languageEnglish (US)
Pages (from-to)1860-1909
Number of pages50
JournalBernoulli
Volume24
Issue number3
DOIs
StatePublished - Aug 2018

Bibliographical note

Funding Information:
The authors thank Tiefeng Jiang and Gongjun Xu for helpful discussions. The second author’s work is partially supported by NSF DMS-13-08270. The third author’s work is partially supported by NSF DMS-13-10096 and NIH NIBIB R01 EB012547.

Funding Information:
The authors thank Tiefeng Jiang and Gongjun Xu for helpful discussions. The second author?s work is partially supported by NSF DMS-13-08270. The third author?s work is partially supported by NSF DMS-13-10096 and NIH NIBIB R01 EB012547.

Publisher Copyright:
© 2018 ISI/BS.

Keywords

  • Markov chain
  • Monte Carlo
  • Spectral methods
  • Standard errors

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